(Updates with CN's offer of new talks, CEO quote, response from union)

By Solarina Ho

TORONTO, March 21 (Reuters) - Canadian National Railway Co said on Friday that it was prepared to meet one last time with the union representing its conductors, yard workers, and traffic coordinators, if the union agreed to a binding arbitration should talks fail.

The Teamsters Canada Rail Conference (TCRC-CTY), which represents about 3,000 CN Rail workers, had no immediate comment on the offer, but said it would discuss the proposal with local representatives and respond on Saturday.

The offer came after union leaders met on Friday to decide whether to strike or take other action after members narrowly rejected a second tentative contract deal with Canada's biggest railway.

"CN is willing to go back to the bargaining table with TCRC-CTY one last time to achieve a fair settlement," the railway's Chief Executive Officer Claude Mongeau said in a statement late on Friday. "But we can only do that if the union commits upfront to binding arbitration in the event our negotiations fail."

It said the union must respond to its offer by Saturday.

Canada's labor minister, Kellie Leitch, urged CN Rail and union leaders on Friday to seek voluntary arbitration to avert a strike, which she said would damage the economy.

The Teamsters union said on Thursday that its members had rejected the latest agreement by a 51.1 percent margin. The deal was reached last month after the government said it would use back-to-work legislation if necessary to keep the railway operating.

The dispute comes as CN Rail struggles to move 5,500 cars of grain a week to cope with a massive backlog from a record-shattering harvest in 2013. The backlog has been exacerbated by transport disruptions caused by an extremely cold winter.

Montreal-based CN Rail previously said it would prefer to settle unresolved issues through final binding arbitration, a process in which an arbitrator decides the final terms of the contract, and requested a union response by the end of Friday's business day.

The union said that government interference has made it difficult to resolve the conflict.

"CN knows that there is no real fear of a work stoppage because the government will step in, so the outstanding issues never get resolved," the Teamsters said in a statement earlier on Friday, calling the failed ratification "not overly surprising".

The union said the vote failed because workers were unhappy that CN was not respecting contractual rest provisions, an issue it called one of worker safety.

It said that CN had been "violating the collective agreement ... since the first tentative settlement was reached back in October and long before that".

CN's spokesman Mark Hallman declined to comment on the charge.

Labor Minister Leitch said she was "disappointed" by the vote result.

"I urge both parties to consider the best interests of all Canadians and avoid a work stoppage by sending their outstanding issues to voluntary arbitration," she said in a statement.

"A work stoppage at CN would have damaging effects on our economy - negatively impacting hardworking Canadians across the country, including grain farmers in the Prairies, auto workers in Ontario, and forestry workers in Quebec."